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A130049 An inductive sum sequence. 4
0, 3, 6, 7, 17, 12, 32, 20, 51, 29, 72, 39, 97, 50, 127, 63, 161, 77, 197, 92, 236, 108, 279, 126, 327, 145, 378, 166, 432, 188, 489, 211, 550, 235, 614, 260, 681, 286, 751, 313, 826, 341, 906, 371, 989, 402, 1074, 435, 1162, 469, 1252, 504, 1347, 540, 1445, 577 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Complement of A130048. The bisection sequences b(1),b(3),b(5),... and b(2),b(4),b(6),... are strictly increasing, but b(2n)<b(2n-1) for n>=3.

LINKS

Table of n, a(n) for n=1..56.

FORMULA

A130049 is the sequence b defined inductively as follows: Let a(1)=1, a(2)=2, b(1)=0, b(2)=3; for n>=3, let x=Floor(n/2) and y=n-x+1. Then a(n)=least positive integer not among a(1),a(2),...,a(n-1), b(1),b(2),...b(n-1) and b(n)=a(1)+a(2)+...+a(x) if n is even, b(n)=a(y)+a(y+1)+...+a(n) if n is odd.

EXAMPLE

(a(1),a(2),...,a(6))=(1,2,4,5,8,9), so x=4 and b(6)=1+2+4+5=12.

(a(1),a(2),...,a(7))=(1,2,4,5,8,9,10), so y=4 and b(7)=5+8+9+10=32.

CROSSREFS

Cf. A130048, A130050, A130051.

Sequence in context: A227723 A192124 A072773 * A259256 A056703 A113534

Adjacent sequences:  A130046 A130047 A130048 * A130050 A130051 A130052

KEYWORD

nonn

AUTHOR

Clark Kimberling, May 03 2007

STATUS

approved

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Last modified December 3 06:42 EST 2016. Contains 278698 sequences.